Hurwicz model of uncertain linear quadratic optimal control with jump. (English) Zbl 1475.49038
Summary: Based on Hurwicz model of uncertain optimal control model with jump, in this paper, a Hurwicz model of uncertain linear quadratic optimal control with jump is proposed. Then, the necessary and sufficient condition for the existence of optimal control is obtained. Finally, an example is given to illustrate usefulness of the proposed model.
MSC:
| 49N10 | Linear-quadratic optimal control problems |
References:
| [1] | Anderson, B. D. O.; Moore, J. B., Optimal control: Linear quadratic methods (1989), Englewood Cliffs, NJ: Prentice Hall, Englewood Cliffs, NJ |
| [2] | Bismut, J. M., Linear quadratic optimal stochastic control with random coefficients, SIAM Journal on Control and Optimization, 14, 3, 419-444 (1976) · Zbl 0331.93086 · doi:10.1137/0314028 |
| [3] | Bonsoussan, A., A stochastic control of partially observed systems (1992), Cambridge, UK: Cambridge University Press, Cambridge, UK · Zbl 0776.93094 |
| [4] | Chen, S. P.; Li, X. J.; Zhou, X. Y., Stochastic linear quadratic regulators with indefinite control weight costs, SIAM Journal on Control and Optimization, 36, 5, 1685-1702 (1998) · Zbl 0916.93084 · doi:10.1137/S0363012996310478 |
| [5] | Chen, R.; Zhu, Y. G., An optimal control model for uncertain systems with time-delay, Journal of the Operations Research Society of Japan, 56, 4, 243-256 (2013) · Zbl 1295.49019 · doi:10.15807/jorsj.56.243 |
| [6] | Davis, M. H. A., Linear estimation and stochastic control (1977), London, UK: Chapman Hall, London, UK · Zbl 0437.60001 |
| [7] | Deng, L. B., Multidimensional uncertain optimal control of linear quadratic models with jump, Journal of Computational Information Systems, 8, 18, 7441-7448 (2012) |
| [8] | Deng, L. B.; Chen, Y. F., Optimistic value model of uncertain linear quadratic optimal control with jump, Journal of Advanced Computational Intelligence and Intelligent Informatics, 20, 2, 189-196 (2016) · doi:10.20965/jaciii.2016.p0189 |
| [9] | Deng, L. B.; Chen, Y. F., Optimal control of uncertain systems with jump under optimistic value criterion, European Journal of Control, 38, 7-15 (2017) · Zbl 1380.49030 · doi:10.1016/j.ejcon.2017.06.002 |
| [10] | Deng, L. B., & Shen, J. Z. (n.d.). Hurwicz model of uncertain optimal control with jump. Manuscript submitted for publication. · Zbl 1455.49027 |
| [11] | Deng, L. B.; You, Z. Q.; Chen, Y. F., Optimistic value model of multidimensional uncertain optimal control with jump, European Journal of Control, 39, 1-7 (2018) · Zbl 1380.93286 · doi:10.1016/j.ejcon.2017.09.002 |
| [12] | Deng, L. B.; Zhu, Y. G., Uncertain optimal control with jump, ICIC Express Letters, Part B: Applications, 3, 2, 419-424 (2012) |
| [13] | Deng, L. B.; Zhu, Y. G., An uncertain optimal control model with n jumps and application, Computer Science and Information Systems, 9, 4, 1453-1468 (2012) · doi:10.2298/CSIS120225049D |
| [14] | Deng, L. B.; Zhu, Y. G., Uncertain optimal control of linear quadratic models with jump, Mathematical and Computer Modelling, 57, 9-10, 2432-2441 (2013) · Zbl 1286.93202 · doi:10.1016/j.mcm.2012.07.003 |
| [15] | Kalman, R. E., Contribution to the theory of optimal control, Boletin Sociedad Matematica Mexicana, 5, 1, 102-119 (1960) · Zbl 0112.06303 |
| [16] | Li, B.; Zhu, Y. G., Parametric optimal control for uncertain linear quadratic models, Applied Soft Computing, 56, 543-550 (2017) · doi:10.1016/j.asoc.2016.05.053 |
| [17] | Li, B.; Zhu, Y. G.; Chen, Y. F., The piecewise optimisation method for approximating uncertain optimal control problems under optimistic value criterion, International Journal of Systems Science, 48, 8, 1766-1774 (2017) · Zbl 1362.93061 · doi:10.1080/00207721.2017.1282061 |
| [18] | Liu, B. D., Uncertainty theory (2007), Berlin: Springer-Verlag, Berlin · Zbl 1141.28001 |
| [19] | Liu, B. D., Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems, 2, 3-16 (2008) |
| [20] | Liu, B. D., Some research problems in uncertainty theory, Journal of Uncertain Systems, 1, 3-10 (2009) |
| [21] | Liu, B. D., Uncertainty theory: A branch of mathematics for modeling human uncertainty (2010), Berlin: Springer-Verlag, Berlin |
| [22] | Liu, B. D., Why is there a need for uncertainty theory?, Journal of Uncertain Systems, 6, 1, 3-10 (2012) |
| [23] | Sheng, L. X.; Zhu, Y. G.; Hamalainen, T., An uncertain optimal control model with Hurwicz criterion, Applied Mathematics and Computation, 224, 412-421 (2013) · Zbl 1334.93185 · doi:10.1016/j.amc.2013.08.079 |
| [24] | Sheng, L. X.; Zhu, Y. G., Optimistic value model of uncertain optimal control, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 21, Suppl, S75-83 (2013) · Zbl 1322.93064 · doi:10.1142/S0218488513400060 |
| [25] | Wonham, W. M., On a matrix Riccati equation of stochastic control, SIAM Journal on Control and Optimization, 6, 1, 681-697 (1968) · Zbl 0182.20803 · doi:10.1137/0306044 |
| [26] | Wonham, W. M., Random differential equation in control theory, probabilistic method in applied mathematics (1970), New York, NY: Academic Press, New York, NY · Zbl 0227.60005 |
| [27] | Wu, Z.; Wang, X. R., FBSDE with Poisson process and its application to linear quadratic stochastic optimal control problem with random jumps, Acta Automatica Sinica, 29, 6, 821-826 (2003) · Zbl 1498.93793 |
| [28] | Wu, H. Z.; Zhou, X. Y., Characterizing all optimal controls for an indefinite stochastic linear quadratic control problem, IEEE Transactions on Automatic Control, 47, 7, 1119-1122 (2002) · Zbl 1364.49044 · doi:10.1109/TAC.2002.800650 |
| [29] | Xu, X. X.; Zhu, Y. G., Uncertain bang-bang control for continuous time model, Cybernetics and Systems: An International Journal, 43, 6, 515-527 (2012) · Zbl 1331.93228 · doi:10.1080/01969722.2012.707574 |
| [30] | Yan, H. Y.; Zhu, Y. G., Bang-bang control model for uncertain switched systems, Applied Mathematical Modelling, 39, 10-11, 2994-3002 (2015) · Zbl 1443.49030 · doi:10.1016/j.apm.2014.10.042 |
| [31] | Yan, H. Y.; Zhu, Y. G., Bang-bang control model with optimistic value criterion for uncertain switched systems, Journal of Intelligent Manufacturing, 28, 527-534 (2017) · doi:10.1007/s10845-014-0996-2 |
| [32] | Yang, X. F.; Gao, J. W., Uncertain differential games with application to capitalism, Journal of Uncertainty Analysis and Applications, 1, 17, 1-11 (2013) |
| [33] | Zhou, X. Y.; Li, D., Continuous-time mean-variance portfolio selection: A stochastic LQ framework, Applied Mathematics and Optimization, 42, 1, 19-33 (2000) · Zbl 0998.91023 · doi:10.1007/s002450010003 |
| [34] | Zhu, Y. G., Uncertain optimal control with application to a portfolio selection model, Cybernetics and Systems, 41, 7, 535-547 (2010) · Zbl 1225.93121 · doi:10.1080/01969722.2010.511552 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
